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How to change Point Markers in a ListPointPlot3D

I want to show three lists in one ListPointPlot3D plot. Mathematica shows each list with differently colored points. However, I'd like to indicate the different sets using different point markers. How can I do this?

The look of the ListPointPlot3D output can be controlled by manupulating the resulting Graphics3D expression internals. Starting with the lpp3 example given by Bruce, extract the directives for primitives in the graphic.

Any graphics directives replacements you would like can be used. Here I wrapped the new result in Show to also change a display option. SphericalRegion will help prevent 3D graphics from jumping around on you after being rotated to the desired viewing angle.

This example pattern isolates just the list1 data points and gives you tall "unit cuboids" - because the z dimention is streached with respect to x and y to enhance the contours, automatically. See, BoxRatios -> {1, 1, 0.4}